Weekly Photo Challenge: geometry (2)
Geometry in nature this time around: FRACTALSRomanesco Cauliflower: a mathematician’s dream vegetable because it’s a perfect natural example of fractals. A fractal is essentially a pattern that repeats itself infinitely. If you look at this romanesco, you’ll see that every Dr. Seuss-ish green spire is studded with a whole bunch of identical mini-spires, which in turn are made up of even tinier spires – all of which mimic the whole. Infinity is a hard concept to grasp, but this here veggie might help you see it…
The word “fractal” often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. The mathematical concept is difficult to formally define even for mathematicians, but key features can be understood with little mathematical background.
The feature of “self-similarity”, for instance, is easily understood by analogy to zooming in with a lens or other device that zooms in on digital images to uncover finer, previously invisible, new structure. If this is done on fractals, however, no new detail appears; nothing changes and the same pattern repeats over and over, or for some fractals, nearly the same pattern reappears over and over. Self-similarity itself is not necessarily counter-intuitive (e.g., people have pondered self-similarity informally such as in the infinite regress in parallel mirrors or the homunculus, the little man inside the head of the little man inside the head…). The difference for fractals is that the pattern reproduced must be detailed.
…and I keep forgetting to add the link to the post announcing the weekly challenge along with other submissions….